How to rotate object along path path
Since you don't need an animation (the word "rotate" misleaded me), you could do in this way:


create a mesh "triangular" segment (33 vertices in my example), and add a sphere





parent the sphere to the segment, clear its origin









enable vertex duplication: any segment vertex gets a copy of the parented object 





then convert dupli to real, and delete or hide original object






This only works on mesh segments (vertices), and is very simple: let's see if this is enough.

Here is the workflow applied to your file:



To work on paths (curves) you need to use another approach, more like in the answer I suggested in comments above. It's more complicated, but gives a similar result for any shape you give to a curve (even straight lines or "triangular"). And, can be animated.